Analysis of $$\textit{MAP}/\textit{PH}_{1}, \textit{PH}_{2}/2$$ Queue with Working Breakdown, Starting Failure, and Bernoulli Vacation

Ayyappan, G.; Gowthami, R.

doi:10.1007/978-981-19-0471-4_14

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…The existing literature on breakdown queueing theory involves examinations of both the conduct of the client within the queue and the behaviors, and characteristics of the system's servers. These studies present an explanation of queueing systems, including Controlled arrivals, breakdown and repair, Working Breakdown, two-customer and a server subject to breakdown, bulk service queue with server breakdown and multiple vacations, M/M/1 queueing model with working vacation, and two types of server breakdown (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) . Gross D introduced steady-state equations and demonstrated them in certain models (19) .…”

Section: Introductionmentioning

confidence: 99%

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

Therasal,

Thiagarajan

2024

IJST

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Objectives: This study aims at (i) introducing the finite capacity of the interdependent queueing model with breakdown and controllable arrival rates, (ii) calculating the average number of clients in the system, and identifying the expected waiting period of the clients in the system, (iii) dealing with the model descriptions, steady-state equations, and characteristics, which are expressed in terms of , and (iv) analyzing the probabilities of the queueing system and its characteristics with numerical verification of the obtained results. Methods: While providing the input, the arrival rates through faster and slower arrival rates are controlled using the Poisson process. Also, the service provides an exponential distribution. The server provides the service on an FCFS basis. In this article, two types of models are used: and which are the system’s conditions, where represents the number of units present in the queue in which their probability is and . All probabilities are distributed based on the speed of advent using this concept. Then, the steady-state probabilities are computed using a recursive approach. Findings: This paper discovers the number of clients using the system on average and the expected number of clients in the system using the probability of the steady-state calculation. Little’s formula is used to derive the expected waiting period of the clients in the system. Novelty: There are articles connected to the finite capacity of failed service in functioning and malfunctioning, but this takes the initiative to provide a link in connection with the rates of the controllable arrivals and interdependency in the arrival and service processes. Mathematics Subject allocation: 60K25, 68M20, 90B22. Keywords: M/M/1/K Queue Model, Finite Capacity, Breakdown, Controllable Arrival rates, FCFS Queue Discipline

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Section: Introductionmentioning

confidence: 99%

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

Therasal,

Thiagarajan

2024

IJST

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A literature review on retrial queueing system with Bernoulli vacation

Micheal Mathavavisakan,

Indhira

2024

YUGOSLAV J OPERATION

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The retrial phenomenon occurs inherently in a wide range of queueing systems. The majority of retrial queueing models do not account for vacation. However, in practice, retrial queueing systems undergo vacations for maintenance or other reasons. In this study, we provide an in-depth analysis of the many possible retrial queueing systems when Bernoulli vacations are in effect. Moreover, this study outlines the key principles and reviews the relevant literature. The framework of a retrial queue with Bernoulli vacation has numerous applications in computer networking systems, manufacturing and production mechanisms, inventory systems, including network service, mail service and file transfer service, etc. Several retrial queueing systems have been investigated, notably M/M/1, M/M/C, M/G/1, M[X]/G/1, and Geo/G/1. Many other important situations, such as server interruption, feedback, G-queue, impatient customers, priority customers, etc., have been explored in relation to retrial queues with Bernoulli vacation and the results of these investigations are also highlighted. The foremost objective of this study is to help researchers, administrators and technical workers who want to use queuing theory to simulate congestion and need to know where to find details on the right models. Finally, some open problems and potential future lines of survey are also covered.

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Analysis of $$\textit{MAP}/\textit{PH}_{1}, \textit{PH}_{2}/2$$ Queue with Working Breakdown, Starting Failure, and Bernoulli Vacation

Cited by 2 publications

References 13 publications

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

Poisson Input and Exponential Service Time Finite Capacity Interdependent Queueing Model with Breakdown and Controllable Arrival Rates

A literature review on retrial queueing system with Bernoulli vacation

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